1.Doprowadź do postaci a) b) c)d) e) 2. doprowadź do postaci A) b) c)d) e) f).... Question from @gwiazdka1997

gwiazdka1997 @gwiazdka1997

November 2018 1 69 Report

1.Doprowadź do postaci $a \sqrt{2}$
a) $\sqrt{32} - 3 \sqrt{2}$
b) $\sqrt{18} + \sqrt{8}$
c) $\sqrt{200} - \sqrt{50}$
d) $\sqrt{18} + \sqrt{72} + \sqrt{98}$
e) $\sqrt{800} + \sqrt{242} - \sqrt{162}$

2. doprowadź do postaci $a\sqrt{b}$
A) $7\sqrt{5} + \sqrt{20}$
b) $\sqrt{48} - \sqrt{3}$
c) $\sqrt{12} + \sqrt{27}$
d) $\sqrt{45} - \sqrt{125}$
e) $0,2\sqrt{50} + 0,8 \sqrt{72} - 0,3 \sqrt{32}$
f) $3 \sqrt{20} - \frac{1}{3} \sqrt{45} -5 \sqrt{180}$

Alexsandrixonka zadanie 1

$postac: \ a\sqrt{2}$

a)

$\sqrt{32} -3 \sqrt{2}= \sqrt{16*2} -3 \sqrt{2}=4 \sqrt{2} -3 \sqrt{2} =1 \sqrt{2}$

b)

$\sqrt{18} + \sqrt{8}= \sqrt{9*2}+ \sqrt{4*2}=3 \sqrt{2}+2 \sqrt{2}=5 \sqrt{2}$

c)

$\sqrt{200}- \sqrt{50}=\sqrt{100*2}-\sqrt{25*2}=10\sqrt{2}-5\sqrt{2}=5\sqrt{2}$

d)

$\sqrt{18}+ \sqrt{72}+ \sqrt{98}= \sqrt{9*2}+ \sqrt{36*2}+ \sqrt{49*2}=\\3 \sqrt{2}+6 \sqrt{2}+7 \sqrt{2}=16 \sqrt{2}$

e)

$\sqrt{800}+ \sqrt{242}- \sqrt{162}= \sqrt{400*2}- \sqrt{121*2}- \sqrt{81*2}=\\20\sqrt{2}-11\sqrt{2}-9\sqrt{2}=0 \sqrt{2}$

zadanie 2

$postac: \ a\sqrt{b}$

a)

$7\sqrt{5}+\sqrt{20}=7\sqrt{5}+\sqrt{4*5}=7\sqrt{5}+2\sqrt{5}=9\sqrt{5}$

b)

$\sqrt{48}-\sqrt{3}=\sqrt{16*3}-\sqrt{3}=4\sqrt{3}-1\sqrt{3}=3\sqrt{3}$

c)

$\sqrt{12}+\sqrt{27}=\sqrt{4*3}+\sqrt{9*3}=2\sqrt{3}+3\sqrt{3}=5\sqrt{3}$

d)

$\sqrt{45}-\sqrt{125}=\sqrt{9*5}-\sqrt{25*5}=3\sqrt{5}-5\sqrt{5}=-2\sqrt{5}$

e)

$0,2\sqrt{50}+0,8\sqrt{72}-0,3\sqrt{32}=\\0,2\sqrt{25*2}+0,8\sqrt{36*2}-0,3\sqrt{16*2}=\\0,2*5\sqrt{2}+0,8*6\sqrt{2}-0,3*4\sqrt{2}=\\1\sqrt{2}+4,8\sqrt{2}-1,2\sqrt{2}=4,6\sqrt{2}$

f)

$3\sqrt{20}-\frac{1}{3}\sqrt{45}-5\sqrt{180}=3\sqrt{4*5}-\frac{1}{3}\sqrt{9*5}-5\sqrt{36*5}=\\3*2\sqrt{5}-\frac{1}{3}*3\sqrt{5}-5*6\sqrt{5}=6\sqrt{5}-1\sqrt{5}-30\sqrt{5}=-25\sqrt{5}$

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